The problem I am working on is:
Express each of these statements using quantifiers. Then form the negation of the statement, so that no negation is to the left of a quantifier. Next, express the negation in simple English. (Do not simply use the phrase “It is not the case that.”)
a) Some old dogs can learn new tricks. b)No rabbit knows calculus.
c) Every bird can fly.
d)There is no dog that can talk.
e) There is no one in this class who knows French and Russian.
I am having trouble with only two parts--namely, d) and e)
For d): $P(x)= x$ cannot talk
$\exists xP(x)$ Negating this, $\neg \exists xP(x) \rightarrow \forall x \neg P(x)$
This would read in English, "Every dog can talk". However, the answer is, "There is a dog that talks."
For e): $F(x)= x$ doesn't know French.$\qquad R(x)= x$ doesn't know Russian.
$\forall x(F(x) \wedge R(x)$ Negating this, $\neg \forall x(F(x) \wedge R(x) \rightarrow \exists x(\neg F(x) \vee \neg R(x))$ Translating this back into English: There is a person in class that knows French or Russian."
However the answer is, "There is someone in this class who knows French and Russian"